Show that the 13th of a month falls more frequently on Friday than on any other day.

See Here
(the calendar has a 400 year cycle, and the frequencies need to be computed
over such a cycle - the intuitive equiprobability model for date/day distribution
is broken up by the leap/non-leap rules for years divisible by 100).

See Here
(the calendar has a 400 year cycle, and the frequencies need to be computed
over such a cycle - the intuitive equiprobability model for date/day distribution
is broken up by the leap/non-leap rules for years divisible by 100).

RonL

What is special about 13 and friday? Can't the same question be asked by replacing 13 by 12 and/or friday by any other day?

Its a property of the Gregorian Calendar, IIRC doesn't happen in the Julian
Calendar.

RonL

I have a doubt. Let January1 of 2001 falls on monday(I don't know exactly).
Then in the cycle of 400 years 13th of a month falls frequently on fridays.
If it would have been tuesday instead of monday, then 13th of a month would have fallen on saturdays(right????).
So it is just of trivial importance that we have January1 on such a day that 13th of a month falls on fridays. It has nothing to do with the probability. It is a fact that friday and 13 are good friends due to the day we assigned to January1 of 2001.
I hope you understand what I want to say.

I have a doubt. Let January1 of 2001 falls on monday(I don't know exactly).
Then in the cycle of 400 years 13th of a month falls frequently on fridays.
If it would have been tuesday instead of monday, then 13th of a month would have fallen on saturdays(right????).
So it is just of trivial importance that we have January1 on such a day that 13th of a month falls on fridays. It has nothing to do with the probability. It is a fact that friday and 13 are good friends due to the day we assigned to January1 of 2001.
I hope you understand what I want to say.

Yes I understand, and yes a shift of 1 day in the phase of the calendar
would result in a different day having the greatest frequency of being
the 13th of the month.